Assad tossed 6 1/3 scoreless innings, conceding just one hit and one walk while striking out five batters to keep Chicago competitive.
"You can do everything in your power to stay healthy, but sometimes all it takes is landing weird once," said Taillon.
"I'm proud of the work I do in between starts to make myself available and out there, but sometimes you just can't avoid it."
Cubs manager Craig Counsell praised Assad's unexpected length and effectiveness from the bullpen, which kept the game deadlocked at 1-1 until extra innings.
"It's a shame, because you lose your starter in the first, and you're kind of going, 'Oh no,' and then you get an outing like that," said Counsell.
"A great outing.
And he deserves to be the hero tonight pitching like that, and we just couldn't make enough happen offensively."
Missed Opportunities
Chicago failed to capitalize on multiple scoring opportunities, including a bases-loaded threat in the fourth inning and a crucial base-running mistake in the eighth inning.
Pinch-runner Kevin Alcántara was doubled off third base following an Alex Bregman lineout to first baseman Rafael Devers, ending a primary scoring threat with no outs.
"I was ready to score," said Alcántara. "There was a bit of confusion there with the bat broken, and I was just very aggressive.
No excuse. I feel like I could've done a much better job to go back to third."
San Francisco broke the tie in the top of the 10th inning when Chapman hit an RBI single off Cubs pitching to drive home ghost runner Jonah Cox.
